Hmm, not off hand. I'll see what I can find. It was my understanding from the hanging chad situation in Florida years ago that, at least in the states, most are initially counted by machine.

Edit: Here you go. I couldn't find research or a study regarding it but this is probably good enough and was always my experience when I voted by paper: https://www.wired.com/2016/11/vote-counts-ballot-get-counted...